Question: Solve for $x$ and $y$ using elimination. ${3x-2y = -3}$ ${5x+2y = 43}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $8x = 40$ $\dfrac{8x}{{8}} = \dfrac{40}{{8}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {3x-2y = -3}\thinspace$ to find $y$ ${3}{(5)}{ - 2y = -3}$ $15-2y = -3$ $15{-15} - 2y = -3{-15}$ $-2y = -18$ $\dfrac{-2y}{{-2}} = \dfrac{-18}{{-2}}$ ${y = 9}$ You can also plug ${x = 5}$ into $\thinspace {5x+2y = 43}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ + 2y = 43}$ ${y = 9}$